Mental Nuts-- Can You Crack 'em?

[footfootfoot]

Originally Posted by classicman

If the hunter circles the tree and the squirrel is STATIONARY ON the tree, then the hunter circles the squirrel.

The earth does not orbit mercury

Maybe this experiment will help: you will need someone to play the squirrel and you will need a piece of rope.

Premise: If you go around someone or something with a piece of rope (with one end of the rope affixed to the someone or something, the other end in your hand) then when you have made a complete circle they will have one turn of rope wrapped around them. Do you agree?

If you do not encircle them then there will be no rope wrapped around them. Do you agree?

Now, try going around your pretend squirrel with one end of the rope in your hand and the other affixed to the squirrel. If the squirrel is stationary you will encircle the squirrel with the rope.
Now try the same thing only this time, the squirrel always turns in the same direction as you. For added realism you can do this outside around a tree. See how many times you managed to encircle the squirrel with the rope.

Have someone record a video of it and put it up on youtube.

[BigV]

Originally Posted by footfootfoot

The earth does not orbit mercury

Maybe this experiment will help: you will need someone to play the squirrel and you will need a piece of rope.

Premise: If you go around someone or something with a piece of rope (with one end of the rope affixed to the someone or something, the other end in your hand) then when you have made a complete circle they will have one turn of rope wrapped around them. Do you agree?

If you do not encircle them then there will be no rope wrapped around them. Do you agree?

Now, try going around your pretend squirrel with one end of the rope in your hand and the other affixed to the squirrel. If the squirrel is stationary you will encircle the squirrel with the rope.
Now try the same thing only this time, the squirrel always turns in the same direction as you. For added realism you can do this outside around a tree. See how many times you managed to encircle the squirrel with the rope.

Have someone record a video of it and put it up on youtube.

But no one, except you, perhaps, define how to make a circle this way, where both ends are moving.

I, and some others, I daresay, define a circle (in this vernacular, vulgar example) as a closed path lying in a plane, with a center and a stationary radius. The area swept by the radius is "inside" the circle, the path traced by the other end of the radius not at the center "is" the circle and everything else beyond the distance of the radius is "outside" the circle.

Stuff inside the circle has been circled.

In your illustration, there are an infinite number of ways to get a turn of rope around the squirrel. And, yes, I can clearly see the situation you describe, and the squirrel won't be encircled. I see that. In your illustration NOTHING will have been encircled, not even the tree. Are you saying that by "attaching one end of the rope to the squirrel" that the tree escapes too?

[jimhelm]

Originally Posted by footfootfoot

The earth does not orbit mercury

Maybe this experiment will help: you will need someone to play the squirrel and you will need a piece of rope.

Premise: If you go around someone or something with a piece of rope (with one end of the rope affixed to the someone or something, the other end in your hand) then when you have made a complete circle they will have one turn of rope wrapped around them. Do you agree?

If you do not encircle them then there will be no rope wrapped around them. Do you agree?

Now, try going around your pretend squirrel with one end of the rope in your hand and the other affixed to the squirrel. If the squirrel is stationary you will encircle the squirrel with the rope.
Now try the same thing only this time, the squirrel always turns in the same direction as you. For added realism you can do this outside around a tree. See how many times you managed to encircle the squirrel with the rope.

Have someone record a video of it and put it up on youtube.

this is a bit of a straw man. you would need to anchor the other end of the rope to the tree in order to be analogous to the problem at hand.